Square Foot Gardening is the practice of planning small but intensively planted gardens.--Thank you Wikipiedia
The original square-foot-gardening method used an open-bottomed box to contain a finite amount of soil, which was divided with a grid into sections. To encourage variety of different crops over time, each square would be planted with a different kind of plant, the number of plants per square depending on an individual plant's size. A single tomato plant might take a full square, as might herbs such as oregano, basil or mint, while most strawberry plants could be planted four per square, with up to sixteen radishes per square. Tall or climbing plants such as maize or pole beans might be planted in a northern row (south in the southern hemisphere) so as not to shade other plants, and supported with lattice or netting.
The logic behind using smaller beds is that they are easily adapted, and the gardener can easily reach the entire area, without stepping on and compacting the soil.
Basically all you need is a spot to grow (can be in the ground or raised with wood or cinder blocks for the sides), soil, string (to make your squares), nails/screws (to hold down the string) seeds and a means to water the garden. It really is that easy. The more it grows, the more you will learn, like how to get rid of bugs that eat your plants (tip: Plant Marigolds all throughout the garden, it helps keep the bugs away).
Next up, container gardening...